Fractal range of a 3-point ternary interpolatory subdivision scheme with two parameters

Zheng, Haibin; Zheng-lin, YE; Zuo-ping, Chen; Zhao, Hongxing

doi:10.1016/j.chaos.2005.12.017

Cited by 14 publications

(4 citation statements)

References 13 publications

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“…Let denote the length of a vector v and , then we get This implies The sum of the length of all the small edges between and after k subdivision steps grows without bound when k approaches to infinity, so by Zheng et al. ( 2007a , ( 2007b ) the limit curve of 6-point scheme is a fractal curve in the range . …”

Section: Fractal Properties Of the Schemementioning

confidence: 99%

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Engineering images designed by fractal subdivision scheme

2016

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This paper is concerned with the modeling of engineering images by the fractal properties of 6-point binary interpolating scheme. Association between the fractal behavior of the limit curve/surface and the parameter is obtained. The relationship between the subdivision parameter and the fractal dimension of the limit fractal curve of subdivision fractal is also presented. Numerical examples and visual demonstrations show that 6-point scheme is good choice for the generation of fractals for the modeling of fractal antennas, bearings, garari’s and rock etc.

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Section: Fractal Properties Of the Schemementioning

confidence: 99%

“…Zheng et al. ( 2007a , b ) analyzed fractal properties of 4-point binary and three point ternary interpolatory subdivision schemes. Wang et al.…”

Section: Introductionmentioning

confidence: 99%

Engineering images designed by fractal subdivision scheme

2016

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“…Furthermore, the subdivision scheme is important not only in the geometric design of smooth curves, but also in the construction of irregular shapes. Zheng et al [11,12] proved that the limit curves generated by binary 4-point and ternary 3-point interpolation subdivision schemes are fractals. Siddiqi et al [13,14] described the fractal behavior of ternary 4-point interpolation subdivision schemes.…”

Section: Introductionmentioning

confidence: 99%

Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme

Peng

Tan

et al. 2018

MCA

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In this paper, a ternary 4-point rational interpolation subdivision scheme is presented, and the necessary and sufficient conditions of the continuity are analyzed. The generalization incorporates existing schemes as special cases: Hassan–Ivrissimtzis’s scheme, Siddiqi–Rehan’s scheme, and Siddiqi–Ahmad’s scheme. Furthermore, the fractal behavior of the scheme is investigated and analyzed, and the range of the parameter of the fractal curve is the neighborhood of the singular point of the rational scheme. When the fractal curve and surface are reconstructed, it is convenient for the selection of parameter values.

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“…Siddiqi and Rehan (2010b) modified the ternary 3-point approximating subdivision scheme that generates family of C 1 and C 2 limiting curves. Zheng et al (2007) analyzed the fractal range of a ternary 3-pointinterpolating subdivision scheme introduced by Hassan and Dodgson (2003). Zheng et al (2005) also presented a ternary 3-point interpolating subdivision scheme that generates C 1 limiting curves.…”

Section: Introductionmentioning

confidence: 99%

A Univariate Symmetric C<sup>5</sup> Subdivision Schem

Siddiqi¹,

Rehan²

2014

RJASET

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Subdivision schemes play a vital role in Computer Aided Geometric Design these days. A new univariate symmetric ternary 6-point approximating subdivision scheme has been introduced that generates the limiting curve of C 5 continuity and its limit functions has a support on (-9, 8). The Laurent polynomial method has been used to investigate the continuity of the subdivision scheme. To determine the maximum degree of smoothness of the subdivision scheme, Holder exponent of the scheme has been calculated. The behavior of the proposed subdivision scheme has been depicted through four examples.

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Fractal range of a 3-point ternary interpolatory subdivision scheme with two parameters

Cited by 14 publications

References 13 publications

Engineering images designed by fractal subdivision scheme

Engineering images designed by fractal subdivision scheme

Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme

A Univariate Symmetric C<sup>5</sup> Subdivision Schem

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